Search

The paper deals with the small scale yielding estimation of nonlinear stresses and strains at the root of sharp and blunt notches through the mechanical model of antiplane shear loadings. The frame stems from the relation existing between the elastic and plastic averaged strain energy densities evaluated over the control volume drawn by the energy contour lines ahead of the notch tip. The analysis proves that there exist different relationships in terms of point-wise elastic and plastic stresses and strains at the notch tip depending whether the notch is sharp (small notch tip radius) or blunt. For sharp notches, the analysis confirms previous results obtained by the present authors, according to which . This equation accounts for the influence of the material law through the hardening exponent n. Differently, when the notch can be regarded as blunt, calculations over the control volume give , in agreement with the Neuber rule.

We study the phenomenon of a spatial localization of elastic waves in periodic composite materials with local defects. The wave spectrum in heterogeneous composite solids includes pass and stop frequency bands. If the frequency of the signal falls within a stop band, the group velocity vanishes and the wave attenuates exponentially. In such a case, a local perturbation of the microstructure may lead to the localization of the wave energy in the vicinity of the defect. Longitudinal tension-compression waves in a layered composite and transverse antiplane shear waves in a unidirectional fibrous composite are considered. Local perturbations of the density and of the volume fractions of the components are taken into account. The analysis is based on the transfer-matrix method and on the plane-wave expansions method. As the result, the frequencies of the wave localization and the corresponding attenuation factors are determined.

The problem of diffraction of antiplane shear waves by a crack of finite length under the permeable electric boundary conditions is investigated analytically. Using Fourier transforms the mixed boundary value problem is reduced to two pairs of dual integral equations. These dual integral equations are further reduced to a pair of Fredholm integral equations of the second kind. The iterative solutions of the Fredholm integral equations have been obtained for small values of the wave number. And analytical expressions for the dynamic stress intensity factor and electric displacement intensity factor are obtained. Finally the numerical results for dynamic stress intensity factor are displayed graphically.

A cracked orthotropic elastic strip of finite width is analyzed under antiplane shear loading. For four frequently encountered constraint edges, i.e. free-free, clamped-clamped, free-clamped, or clamped-free edges, the Fourier series method is used to reduce triple series equations, and then to a mixed boundary value problem associated with a mode-III crack for each case to a singular integral equation. Closed-form solutions are derived for the resulting equations, and formulae for calculating stress intensity factors are obtained for an internal crack and edge cracks subjected to arbitrarily varying loading. Numerical results of the stress intensity factors for an eccentric, central, and edge crack are shown graphically for the case of uniform loading at the crack faces. Obtained formulae for determining stress intensity factors can be taken as a benchmark of numerical evaluations. The derived results are also applicable to an isotropic elastic strip with an anti-plane shear crack normal to the edges.

Based on the Lekhnitskii-Eshelby approach of two-dimensional anisotropic elasticity, a semi-analytical solution is derived for the problem associated with an anisotropic elliptical inhomogeneity embedded in an infinite anisotropic matrix subjected to remote uniform antiplane shear stresses. In this research, the linear spring type imperfect bonding conditions are imposed on the inhomogeneity-matrix interface. We use a different approach than that developed by Shen et al. (2000) to expand the function encountered during the analysis for an imperfectly bonded interface. Our expansion method is in principle based on Isaac Newton's generalized binomial theorem. The solution is verified, both theoretically and numerically, by comparison with existing solution for a perfect interface. It is observed that the stress field inside an anisotropic elliptical inhomogeneity with a homogeneously imperfect interface is intrinsically nonuniform. The explicit expression of the nonuniform stress field within the inhomogeneity is presented. The nonuniform stress field inside the inhomogeneity is also graphically illustrated. A difference in internal stress distribution between a composite composed of anisotropic constituents and a composite composed of isotropic constituents is also observed. We finally extend the solution derived for a linear spring type imperfect interface to address an elliptical inhomogeneity with a viscous interface described by the linear law of rheology. It is observed that the stress field inside an elliptical inhomogeneity with a viscous interface is nonuniform and time-dependent.

In this paper, we employ the regularized meshless method to solve antiplane shear problems with multiple inclusions. The solution is represented by a distribution of double-layer potentials. The singularities of kernels are regularized by using a subtracting and adding-back technique. Therefore, the troublesome singularity in the method of fundamental solutions (MFS) is avoided and the diagonal terms of influence matrices are determined. An inclusion problem is decomposed into two parts: one is the exterior problem for a matrix with holes subjected to remote shear, the other is the interior problem for each inclusion. The two boundary densities, essential and natural data, along the interface between the inclusion and matrix satisfy the continuity and equilibrium conditions. A linear algebraic system is obtained by matching boundary conditions and interface conditions. Finally, numerical results demonstrate the accuracy of the present solution. Good agreements are obtained and compare well with analytical solutions and Gong's results.

An elastodynamic analysis of an interface crack in coated media with functionally graded properties is performed under the condition of antiplane shear impact. The graded material exists as a nonhomogeneous interlayer between the dissimilar, homogeneous phases of the coating/substrate system or as a nonhomogeneous coating deposited on the substrate. The material nonhomogeneity is represented in terms of power-law variations of shear modulus and mass density. Based on the use of the integral transform technique, formulation of the transient crack problem is reduced to having to solve a Cauchy-type singular integral equation in the Laplace transform domain. Via the inversion of the Laplace transforms, the values of dynamic mode III stress intensity factors are obtained as a function of time. In the numerical results, the effects of material and geometric parameters of the coating/substrate system with the graded, nonhomogeneous constituent are illustrated, addressing the dynamic load transfer and overshoot characteristics of the transient crack-tip behavior. Furthermore, a comparison is made with the dynamic behavior of the interface crack in a discretely coated material system.

The effect of surface stress on the size-dependent interaction of a screw dislocation with a circular nano-hole under remote antiplane shear loads is examined. By using the complex variable method, the analytical expressions of the complex potential in infinite matrix and the image force acting on the screw dislocation are obtained. The associated solutions to the problem of a screw dislocation interacting with a nano-inhomogeneity are also given. The results show that the influence of the surface stress on the motion of the dislocation near the hole becomes remarkable when the size of the hole is reduced to nanometer scale, leading to that the normalized image force depends on the hole size which differs from the size-independent classical elastic solution. Our results are helpful in the understanding of the motion mechanism of the dislocation and relevant physical phenomena in nano-structured materials. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

A finite element formulation is developed to determine the order and angular variation of singular stress states at material and geometric discontinuities in anisotropic materials subject to antiplane shear loading. The displacement field of the sectorial element is quadratic in the angular co-ordinate direction and asymptotic in the radial direction measured from the singular point. The formulation of Yamada and Okumura14 for in-plane problems is adapted for this purpose. The simplicity and accuracy of the formulation are demonstrated by comparison to several analytical antiplane shear solutions for both isotropic and anisotropic multi-material wedges and junctions with and without disbonds. The nature and speed of convergence of the eigensolution suggests that the solution presented here could be used in developing enriched elements for accurate and computationally efficient evaluation of stress intensity factors in problems having complex global geometries.

We apply the nonlinear dislocation theory to the problem of antiplane constrained shear in a single crystal with one slip system. By taking dissipation into account, the relaxed energy functional has to be minimized. We show that, up to a threshold strain, no dislocations are nucleated and therefore the plastic slip is zero. Since this threshold value depends on the width of the specimen, a size effect takes place. The stress strain curve turns out to be a hysteresis loop exhibiting the work hardening due to the dislocation pile-up. It is shown that the Bauschinger effect holds true. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Under the assumption that the motion of the body cases only weak perturbations in the electromagnetic field, the scattering of horizontally polarized shear waves by a finite crack in a uniform magnetostatic field is considered for two cases of the magnetic field being parallel to the crack surfaces and perpendicular to the crack surfaces. It is assumed that the elastic medium under consideration is a homogeneous, isotropic and infinitely conducting one. Using an integral transform technique, the problem is reduced to that of solving a Fredholm integral equation of the second kind having the kernel of a finite integration which can be solved numerically by the use of Gaussian quadrature formulas. By obtaining the singular stress distributions near the crack tip and dynamic stress-intensity factors, the effects on the stress-intensity factors due to the presence of the magnetic field are shown graphically. For the low frequencies, the stress-intensity factors are expressed in series of ascending powers of the normalized frequency. The approximate solutions are compared with exact solutions. Es wird angenommen, das die Bewegung eines Korpers im elektromagnetischen Feld nur schwache Storungen verursacht. Unter dieser Voraussetzung wird die Streuung horizontal polarisierter Scherwellen, hervorgerufen durch einen endlichen Sprung in einem magnetischen Feld, fur 2 Falle betrachtet: (a) Magnetfeld parallel zur Sprungebene, (b) Magnetfeld senkrecht zur Sprungebene. Das betrachtete elastische Medium sei homogen, isotrop und ideal leitend. Durch die Anwendung einer Integraltransformation wird das Problem auf die Losung einer Fredholmschen Integralgleichung 2. Art zuruckgefuhrt, deren Kern – ein endliches Integral – numerisch mittels der Gausschen Quadraturformeln berechnet werden kann. Es ergeben sich die singularen Spannungsverteilungen in der Nahe des Sprunges und die dynamischen Spannungsintensitatsfaktoren. Dadurch last sich die Wirkung des Magnetfeldes auf die Spannungsintensitatsfaktoren graphisch darstellen. Fur niedere Frequenzen werden die Spannungsintensitatsfaktoren in einer Reihe nach steigenden Potenzen der normalisierten Frequenzen angegeben. Die Naherungslosungen werden mit den exakten Losungen verglichen.

Scattering of antiplane shear waves (SH) in two dimensions by surface and near-surface defects in a homogeneous, isotropic elastic semi-infinite medium has been studied. Attention has been focused here in the range of medium to long wavelengths. A combined finite element and analytical technique has been used to study the problems of scattering by semi-circular and triangular canyons. The results for the former case are compared with the known exact solution and those for the latter case are compared with some available approximate solutions. Finally a problem of multiple scattering by a triangular canyon and a nearby circular tunnel is studied. Numerical results are presented showing the effects of multiple scattering and different angles of incidence. These results are of interest in earthquake engineering.